A Resolution of the Fisher Effect Puzzle: A Comparison of Estimators.

A Resolution of the Fisher Effect Puzzle: A Comparison of Estimators Ekaterini Panopoulou∗ National University of Ireland, Maynooth and University of Piraeus, Greece February 2005 Abstract This paper attempts a resolution of the Fisher effect puzzle in terms of estimator choice. Using both short-term and long-term interest rates for 14 OECD countries, we find ample evidence supporting the existence of a long-run Fisher effect in which interest rates move oneto-one with inflation. Our results suggest that the reason why the Fisher effect has not found support internationally lies on the estimation method. When the hypothesis of a unit coefficient relating interest rates to expected inflationistestedwithintheAutoregressiveDistributedLag (ADL) framework, which is invariant to the integration properties of the data, the Fisher effect easily survives the empirical evidence. Similar, but less robust, results are reached on the grounds of the Pre-Whitened Fully Modified Least Squares (PW-FMLS) or the Johansen’s (JOH) estimators. JEL Classification: E40; E50; C12; C13; Keywords: Cointegration Estimators; Fisher Effect; ADL; DOLS; Small-sample properties Acknowledgments: Financial support from the Greek Ministry of Education and the European Union under “Hrakleitos” grant is greatly appreciated. I am grateful to A. Antzoulatos, S. Kalyvitis, G.Hardouvelis, D. Malliaropulos, M. Roche, M. Hurley, N.Pittis, D. Thomakos, E. Tzavalis and seminar participants at the IIIS Miniconference on International Financial Integration, National University of Ireland and the University of Peloponesse for helpful suggestions and comments. The usual disclaimer applies. ∗Correspondence to: Ekaterini Panopoulou, Department of Economics, National University of Ireland Maynooth, Co.Kildare, Republic of Ireland. E-mail: [email protected]. Tel: 00353 1 7083793. Fax: 00353 1 7083934. 1 1 Introduction A vast literature is devoted to the size of the response of nominal interest rates to changes in expected inflation, broadly known as the Fisher effect.1The monetary neutrality implications for different Fisher effect values underlie this long-standing interest in the topic. More specifically, long-run superneutrality of money is associated with a coefficient relating interest rates to expected inflation equal to one, while a value below unity implies substantial long-run non-neutralities. In this vein, the stationarity of the ex-ante real interest rate has some important implications. As suggested by the standard consumption asset pricing model, real interest rates should follow the pattern of consumption growth, which is clearly a stationary variable. Moreover, the neoclassical growth theory based on dynamic optimization for a representative economic agent implies that the real rate should be constant in the steady state, being proportional to the representative consumer’s rate of time preference. Unfortunately there is no consensus among economists about the true size of the Fisher effect. There are several problems that plague empirical estimates of the Fisher effect. Darby (1975) introduced the effect of taxes on the size of the Fisher effect. He argued that nominal interest rates should increase by more than the increase in expected inflation to compensate debt holders for a lower after-tax return since interest income is usually taxed as ordinary income. In this case, we should obtain a Fisher effect estimate greater than one. A second problem is the generally unobserved nature of the expected inflation rate. When actual realized inflation is used to proxy expected inflation an errors-in-variables bias is introduced on the estimate of the Fisher effect. Another issue involves the time series properties of the data under consideration when estimating a relationship like the Fisher effect. The only case that standard least squares techniques are valid is when the series are second-order stationary. In the event of integrated variables, the only way to establish a theoretical Fisher relationship is via cointegration techniques. Finally, even when applying the appropriate cointegration methods, severe problems may arise associated with the implementation of cointegration, such as the low power of cointegration tests or the performance of the various estimators in small samples. Crowder and Hoffman (1996) suggested that the estimator choice might account for the contradictory evidence in the literature. Specifically, the authors attribute the different conclusions reached in the literature regarding the relationship between inflation and interest rates to the differences in the small sample properties of the Ordinary Least Squares (OLS), the Dynamic Least Squares (DOLS) and the Johansen’s (JOH) maximum likelihood estimators. More recently, Caporale and Pittis (2004) show that the estimators frequentlyemployedinempiricalstudies,namelyOLS and Fully Modified Least Squares (FMLS), are the ones with the least desirable small 1See e.g. Cooray, 2003 and the references therein. 2 sample properties. The inability of these estimators to provide efficient estimates in small samples is likely to be responsible for the overrejection of the Fisher hypothesis. Specifically, the authors show that when the estimators with the best properties are chosen, the evidence is strongly supportive of the Fisher effect in the US. In this study, we use both short-term and long-term interest rates and provide international evidence on a long-run Fisher effect, i.e. that interest rates and inflation move one-to-one in the long-run for 14 OECD countries. Using a variety of asymptotically efficient cointegration estimators we attempt to explain the Fisher effect puzzle in terms of estimator choice. We attribute the scarce evidence of an international Fisher effect in the literature to the poor small sample performance of the estimators employed so far. We particularly focus on two types of cointegration estimators that arise in the context of the Hendry-style Autoregressive Distributed Lag (ADL) models. The first type is usually referred to as the DOLS estimator (see Stock and Watson, 1993) and arises from a static cointegration equation augmented by current and past values of the first difference of the regressor. The second type, the ADL estimator (see Pesaran and Shin, 1999), is based on the projection of the cointegration error on the full information set, i.e. the current and past values of the first difference of the regressor plus the past values of the cointegration error. In an extensive Monte Carlo study, Panopoulou and Pittis (2004) highlighted the potential pitfalls of employing the DOLS estimator as opposed to the ADL one in small samples for a wide variety of Data Generation Processes (DGPs). The authors showed that the ADL estimator, which utilizes the exact projection of the cointegration error on the full information set, offers a better framework for estimating the cointegration vector than the DOLS estimator that utilizes an approximate projection of the cointegration error on information provided only by the error that drives the regressor. To this end, the behavior of the ADL estimator seems to be the limiting one of the DOLS estimator. For comparison purposes, we also include some other commonly used cointegration estimators, such as the OLS and the semiparametric FMLS estimator of Phillips and Hansen (1990) and the Johansen’s maximum likelihood estimator (1988, 1991). The layout of this paper is as follows: Section 2 provides a brief literature review on the Fisher effect and a discussion of the Fisher equation. Section 3 outlines the econometric methodology used in the empirical analysis. Section 4 presents estimates of the Fisher equation obtained by the ADL and DOLS estimators for both our datasets, along with estimates obtained from the OLS, FMLS and JOH estimators. Section 5 summarizes the main findings of the paper. 2 Brief literature review Ex ante real interest rates appear to be a key variable when investment - savings decisions and asset prices determination are considered. Their long-run behavior is 3 often analyzed in the context of the Fisher (1930) relationship, linking nominal rates to expected inflation and requiring full adjustment of the former to the latter. The importance of this adjustment process stems from the fact that permanent shocks to either inflation or nominal rates should not be translated into permanent disturbances to real rates themselves, which would be problematic in the context of standard models of intertemporal asset pricing. However, thus far the empirical evidence has not been supportive of the Fisher relationship. Numerous studies have found that the slope coefficient in a regression of inflation against nominal rates is significantly different from one, at least over certain periods, (see e.g. Mishkin 1992 and Evans and Lewis, 1995). Formally, the ‘Fisher effect’ can be expressed as: it(m)=πe t(m)+re t(m)(1) where it(m)is the m-period nominal interest rate at time t, πe t(m)denotes the expected rate of inflationfromtimettot+m,andre t(m)is the ex-ante real interest rate. Assuming rational expectations (see, e.g. Mishkin, 1992), realized inflation is linked to expected inflation as follows: πt(m)=πe t(m)+et(2) where etis a white noise process, orthogonal to πe t(m).If we further assume that the process followed by the real interest rate is a white noise process with a mean equal to r, weareabletotestfortheFishereffect in the context of the following regression: it(m)=r+θπt(m)+νt(3) The null hypothesis to be tested can take the form: Fisher hypothesis holds ⇔(i) νtis I(0) and (ii) θ=1. The first of these conditions, i.e. the condition that it(m)and πt(m)are cointegrated processes is supported by the bulk of empirical evidence in the literature. On the other hand, when dealing with the second condition, estimates of θappear to be significantly different from unity, leading to the Fisher effect puzzle. Mishkin (1992) was one of the first to suggest that due to the apparent nonstationarity of nominal interest rates and inflation a possible source of the low Fisher effect estimates is the spurious regression problem discussed by Granger and Newbold (1974). He correctly pointed out that the Fisher relation should be treated within the context of a cointegrated system, as in Engle and Granger (1987). Mishkin used the Engle-Granger OLS procedure to estimate the Fisher effect but did not derive any strong conclusions due to the large standard errors of the estimated parameters. Subsequent studies used more efficient estimation procedures and generally found 4 support for a long-run Fisher relation in the U.S. Evans and Lewis (1995) used the DOLS estimator and Crowder and Hoffman (1996) used the Johansen gaussian maximum likelihood estimator. Crowder and Hoffmann (1996) suggested that the estimator choice might account for the contradictory evidence gathered so far. In particular, the authors argue that differences in the small sample properties of the OLS, DOLS and JOH estimators are responsible for the vastly different conclusions reached in the literature about the relationship between inflation and interest rates. Their analysis, however, was much more limited than ours as they compared only three estimators in terms of small sample bias. More recently, Atkins and Coe (2002) found evidence supporting the long-run Fisher effect for both Canada and the US using a variety of interest rates and the ARDL bounds test developed by Pesaran et.al (2001) which is capable of testing for the existence of a long-run relationship regardless of the integration properties of the underlying series. Fahmy and Kandil (2003) confirmed that inflation and interest rates exhibit common trends in the long-run and move in a one-to-one relation at long horizons, specifically when the assets’ maturity exceeds two years. Their dataset includes, except for US, UK, Germany and Switzerland. Caporale and Pittis (2004) employed virtually all available single-equation estimators and allowed for alternative data frequencies along with structural breaks.2 The authors examined whether (i) differences in the estimate of θfrom one can be attributed to small sample bias and (ii) rejections of the null reflect the use of asymptotic critical values rather than the empirical ones. They found evidence in favor of both claims, which implies that the Fisher hypothesis survives even when less satisfactory estimators are employed provided that the empirical critical values are used. Choosing the estimator with the minimum bias and shift in the distribution of the associated t-statistics, valid inference can be conducted in support of the Fisher identity. However, their study was confined to the US, which is the country usually employed in empirical studies on the Fisher hypothesis. There is some evidence, though, on the nominal interest rates and inflation relationship in other industrialized countries. Testing whether the Fisher relationship holds internationally is of interest since a necessary, but not sufficient, condition for real interest rates to be equalized internationally is that the Fisher relation holds in each country individually. Rose (1988) examined the integration properties of nominal interest rates and inflation for 18 OECD countries. He concluded that inflation does not appear to have a unit root, while nominal interest rates do. By contrast, Koustas and Serletis (1999) examined 10 industrialized countries and established that the conditions for meaningful Fisher effects, i.e. that inflation and interest rates are I(1) and cointegrated processes, hold. The authors, 2These cointegration estimators (most of which are asymptotically efficient) deal with the second order effects (long-run correlation and endogeneity effect) present in the OLS asymptotic distribution, either patrametrically or non-parametrically. 5 however, were not able to provide strong evidence in support of the Fisher hypothesis, i.e. to establish a unit coefficient. 3 Econometric Methodology In this section, we consider two asymptotically efficient cointegration estimators on which our analysis is based, namely the ADL and DOLS estimators. The latter is a widely-used cointegration estimator suggested by Saikonnen (1991), Phillips and Loretan (1991) and Stock and Watson (1993), while the first developed by Pesaran and Shin (1999) is rarely employed in empirical applications despite its superiority in many aspects. Next, we show how these estimators are derived and compare their properties. We also briefly discuss the OLS, FMLS and JOH estimators. To facilitate the discussion, we employ the Phillips triangular representation of a cointegrated system. Let ztand utbe two bivariate processes, with zt=[yt,x t]>and ut=[u1t,u 2t]>. We further assume that utis a VAR(1) process, driven by et=[e1t,e 2t]>and the generating mechanism for ytis given by the system yt=θxt+u1t(4) ∆xt=u2t(5) Ãu1t u2t!=Ãa11 a12 a21 a22 !Ãu1t−1 u2t−1!+Ãe1t e2t!(6) and Ãe1t e2t!˜NIID"Ã0 0!Ãσ11 σ12 σ12 σ22 !# (7) for t=1,2,...T. Both eigenvalues of the matrix A=[aij],i,j =1,2are assumed to be less than one in modulus, in order for ytand xtto be I(1) variables, and the cointegration error to be an I(0) process. The long-run covariance matrix Ωand the one-sided covariance matrix ∆,needed to define the asymptotic nuisance parameters, are given by equations (8) and (9), respectively Ω=(I−A)−1Σ(I−A>)−1(8) ∆=G(I−A>)−1(9) where Σdenotes the innovations covariance matrix of the VAR and Gis the unconditional covariance matrix of utgiven by, vecG =(I−A⊗A)−1vecΣ(10) 6 An early result by Stock (1987) shows that the OLS estimator of θobtained from (4) is super-consistent, regardless of the presence of temporal and/or contemporaneous correlation between the regression error, u1t,and the error that drives the regressor, u2t.On the other hand, in general, the asymptotic distribution of the OLS estimator of θfalls outside the Local Asymptotic Mixture of Normals (LAMN) family and contains nuisance parameters. The reason for the presence of non-standard asymptotics is that in the presence of contemporaneous and temporal correlation between the elements of ut, two types of second-order asymptotic effects are present in the limiting distribution of the OLS estimator (see Phillips and Loretan 1991): The first is the nuisance parameter, ω12/ω22 that describes the “long-run correlation” effect, due to non-diagonality of the long run covariance matrix Ω=[ωij],i,j =1,2.The second is the nuisance parameter δ21 =P∞ k=0 E(u20u1k)that describes the “endogeneity” effect. In order to remove the second order effects parametrically, we must employ a new regression model whose error term is orthogonal to u2tand u2t−i,i=1,2,.... This can be done by employing the conditional expectation of u1teither on the current and past values of u2tor on the current and past values of u2tplus the past values of u1t.The first and second conditioning information sets result in the DOLS and ADL estimators, respectively. Next, we show how these estimators are actually derived, starting from the latter. 3.1 The ADL estimator The full system (4) and (5) with errors specified by (6) - (7), implies the following conditional density of yt: D(yt|xt,z0 t−1,λ 1)=N(θ1xt+c1yt−1+c2xt−1+c3xt−2,σ2 v)(11) where λ1≡(θ1,c 1,c 2,c 3,σ2 v)and θ1=θ+σ12 σ22 (12) c1=a11 −a21 σ12 σ22 (13) c2=a12 −σ12 σ22 (a22 +1−a21θ)−a11θ(14) c3=(a22 σ12 σ22 −a12)(15) σ2 ν=σ11 −σ2 12 σ22 (16) This conditional model can be written as the ADL(q,r)regression, with orders (q,r)= (1,2): yt=θ1xt+c1yt−1+c2xt−1+c3xt−2+νt(17) 7 The new error term, vt, is now orthogonal to u2t,ut−1,ut−2,...and its variance is given by (16). In the context of the ADL(1,2) model the cointegration parameter θis equal to the long-run multiplier of ytwith respect to xt,that is θ=θ1+c2+c3 1−c1 (18) We can estimate (17) by OLS and then use (18) to obtain an efficient estimate of θ. However, additional computations are required to obtain the variance of this estimate (see Banerjee et. al. 1993). A more convenient approach, proposed by Bewley (1979), transforms the model (17) in such a way that a point estimate of θand its variance can be obtained directly. After some algebraic manipulation, model (17) can be equivalently written as: yt=δ0∆yt+θxt+λ0∆xt+λ1∆xt−1+ηt(19) where δ0=−c1 (1−c1)λ0=−c2+c3 (1−c1)λ1=−c3 (1−c1)ηt=1 (1−c1)νt Estimates of the coefficients and their standard errors can be obtained by using the Instrumental Variables (IV) estimator, with the original matrix of regressors, i.e. the variables in (17), being the instrumental variables (see Wickens and Breusch 1988). This means that the ADL estimator of θis very easy to apply since it involves only IV estimation techniques. 3.2 The DOLS estimator The ADL model, derived above, may be thought of as arising from projecting u1ton the full information set B=(u2t,ut−1,ut−2,...),that is E(u1t|B)=σ12 σ22 e2t+a11u1t−1+a12u2t−1(20) As already mentioned, the second-order effects can be dealt with by projecting u1ton a subset of this set, namely A=(u2t,u 2t−1,u 2t−2,...),A⊂B:The resulting conditional expectation involves an infinite sum, E(u1t|A)= ∞ X i=0 βiu2t−i(21) where βiare functions of the parameters in (6)-(7). This conditional expectation does not admit a parsimonious representation analogous to (20). On the other hand, it allows for direct substitution of this expression into (4), thus yielding the following 8 model yt=θxt+ ∞ X i=0 βi∆xt−i+υt(22) where υtis, in general, a serially correlated error term. In particular, υtfollows the AR(1) model υt=γ2υt−1+εt(23) where γ2is the MA coefficient in the ARMA (2,1) representation of u2t.SimpleOLS applied to (22) yields the DOLS(p) estimator of Stock and Watson (1993), where p denotes the lag length of the first differences of the regressor added to (22). The serial correlation of υtdoes not raise any serious problems in the estimation of θ,provided that a consistent estimator of the long-run variance of υtis employed, such as the one proposed by Newey and West (1987). Alternatively, the application of Generalized Least Squares (GLS) on (22), ensures valid asymptotic inferences on θ.3In this case, the estimator in use is the DGLS(p) one. In practice, however, the second term on the right-hand side of (22) has to be replaced by an approximation in which the infinite sum is truncated at i=p.The resulting model accommodates a truncation remainder that is likely to increase the bias of the DOLS(p) estimator of θ. This bias grows with the persistence of the cointegration error. Increasing the truncation point reduces the DOLS bias, but increases its variance. Moreover, estimating (22) by OLS is not feasible if p is too large compared to the sample size. Saikkonen (1991) specifies an upper bound for the rate at which p is allowed to increase with the sample size T, which is given by the condition p3/T →0. Nevertheless, this condition cannot be used to define the optimal value of p for any given sample size. On the contrary, the ADL estimator does not accommodate any truncation remainder and more importantly, yields consistent estimates of the long-run coefficients that are asymptotically normal irrespective of whether the underlying regressors are I(1) or I(0). Finally, it is easy to show that the only case that the ADL and DOLS estimators are equivalent is this of a non-autocorrelated error in (4), which is a highly unlikely case in the case of macroeconomic applications. 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Breusch (1988), Dynamic Specification, the Long Run and the Estimation of Transformed Regression Models, Economic Journal, 98, (Conference 1988), 189-205. 18 19 Appendix: Tables Table 1A: Estimation Results – Quarterly short-term interest rates Country Australia Belgium Canada Estimator θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 OLS 0.411 0.107 -5.537 0.433 0.116 -4.873 0.598 0.118 -3.415 ADL(1,2) 0.721 0.272 -1.028 0.722 0.414 -0.671 0.959 0.199 -0.202 JOH 1.294 0.241 1.218 1.351 0.312 1.124 1.195 0.151 1.291 FMLS 0.499 0.190 -2.628 0.573 0.194 -2.204 0.677 0.138 -2.334 PW-FMLS 0.891 0.204 -0.532 0.971 0.373 -0.079 1.101 0.188 0.535 DOLS 1 0.510 0.121 -4.069 0.509 0.152 -3.235 0.695 0.126 -2.417 DOLS 2 0.563 0.130 -3.360 0.540 0.170 -2.704 0.756 0.132 -1.853 DOLS 3 0.584 0.136 -3.053 0.551 0.183 -2.456 0.786 0.134 -1.592 DOLS 4 0.592 0.141 -2.903 0.548 0.189 -2.389 0.799 0.136 -1.481 DOLS 5 0.597 0.146 -2.770 0.549 0.193 -2.337 0.810 0.135 -1.408 DOLS 6 0.603 0.151 -2.639 0.555 0.190 -2.340 0.813 0.134 -1.391 DOLS 7 0.616 0.155 -2.485 0.570 0.183 -2.350 0.819 0.133 -1.360 DOLS 8 0.629 0.157 -2.365 0.590 0.173 -2.379 0.823 0.133 -1.329 DOLS 9 0.647 0.160 -2.212 0.608 0.166 -2.360 0.835 0.133 -1.235 DOLS 10 0.669 0.162 -2.047 0.620 0.169 -2.244 0.843 0.135 -1.164 DOLS 11 0.692 0.162 -1.897 0.622 0.177 -2.138 0.854 0.137 -1.071 DOLS 12 0.713 0.161 -1.784 0.615 0.185 -2.078 0.862 0.140 -0.991 DOLS 13 0.732 0.160 -1.670 0.617 0.196 -1.959 0.875 0.141 -0.887 DOLS 14 0.754 0.159 -1.546 0.636 0.203 -1.796 0.886 0.142 -0.804 DOLS 15 0.772 0.157 -1.446 0.659 0.211 -1.614 0.895 0.143 -0.734 DOLS 16 0.792 0.156 -1.337 0.687 0.219 -1.426 0.905 0.143 -0.668 DOLS 17 0.811 0.153 -1.233 0.732 0.224 -1.197 0.916 0.142 -0.594 DOLS 18 0.832 0.152 -1.106 0.776 0.225 -0.994 0.923 0.140 -0.554 DOLS 19 0.847 0.152 -1.008 0.813 0.224 -0.835 0.927 0.136 -0.542 DOLS 20 0.853 0.152 -0.968 0.853 0.218 -0.675 0.927 0.133 -0.549 DGLS 1 -0.021 0.055 -18.589 0.095 0.057 -15.950 0.116 0.050 -17.871 DGLS 2 0.153 0.084 -10.139 0.228 0.083 -9.290 0.253 0.074 -10.034 DGLS 3 0.289 0.114 -6.244 0.411 0.108 -5.470 0.406 0.104 -5.735 DGLS 4 0.368 0.132 -4.798 0.368 0.125 -5.075 0.505 0.124 -3.999 DGLS 5 0.364 0.149 -4.259 0.160 0.149 -5.658 0.643 0.137 -2.609 DGLS 6 0.299 0.164 -4.268 0.101 0.165 -5.464 0.581 0.155 -2.702 DGLS 7 0.267 0.182 -4.035 0.056 0.179 -5.277 0.634 0.168 -2.185 DGLS 8 0.184 0.200 -4.076 0.113 0.190 -4.661 0.609 0.179 -2.181 DGLS 9 0.050 0.223 -4.259 0.205 0.201 -3.965 0.706 0.183 -1.613 DGLS 10 0.072 0.240 -3.868 0.325 0.211 -3.198 0.657 0.194 -1.769 DGLS 11 0.195 0.247 -3.263 0.401 0.223 -2.683 0.671 0.203 -1.623 DGLS 12 0.270 0.254 -2.876 0.320 0.233 -2.921 0.609 0.217 -1.807 DGLS 13 0.186 0.275 -2.962 0.179 0.240 -3.417 0.641 0.220 -1.628 DGLS 14 0.376 0.264 -2.361 0.126 0.251 -3.488 0.686 0.227 -1.383 DGLS 15 0.395 0.270 -2.238 0.006 0.267 -3.717 0.629 0.244 -1.520 DGLS 16 0.361 0.285 -2.242 -0.161 0.281 -4.128 0.640 0.254 -1.421 DGLS 17 0.366 0.294 -2.157 -0.255 0.301 -4.170 0.769 0.241 -0.961 DGLS 18 0.498 0.284 -1.772 -0.145 0.319 -3.584 0.837 0.239 -0.683 DGLS 19 0.612 0.278 -1.396 -0.271 0.347 -3.664 0.857 0.244 -0.586 DGLS 20 0.468 0.311 -1.710 -0.169 0.373 -3.135 0.783 0.262 -0.828 Notes 1. The Newey and West (1987) method is employed in the DOLS(p) estimator. 2. An AR(1) model is assumed for the errors in the DGLS(p) estimator. 20 Table 1B: Estimation Results – Quarterly short-term interest rates Country France Germany Ireland Estimator θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 OLS 0.441 0.09 -6.185 0.444 0.095 -5.832 0.488 0.201 -2.544 ADL(1,2) 0.707 0.234 -1.249 0.787 0.366 -0.579 1.278 0.668 0.416 JOH 0.918 0.187 -0.440 1.575 0.157 3.671 1.535 0.854 0.626 FMLS 0.438 0.130 -4.336 0.526 0.157 -3.021 0.749 0.403 -0.621 PW-FMLS 0.627 0.228 -1.637 1.339 0.178 1.910 1.248 0.525 0.471 DOLS 1 0.475 0.094 -5.591 0.631 0.123 -2.995 0.687 0.260 -1.203 DOLS 2 0.492 0.098 -5.168 0.881 0.148 -0.805 0.820 0.269 -0.668 DOLS 3 0.500 0.104 -4.833 0.982 0.163 -0.109 0.840 0.312 -0.511 DOLS 4 0.499 0.110 -4.547 0.968 0.169 -0.192 0.773 0.330 -0.688 DOLS 5 0.505 0.116 -4.284 0.938 0.174 -0.355 0.795 0.310 -0.662 DOLS 6 0.507 0.120 -4.106 0.907 0.176 -0.528 0.814 0.307 -0.604 DOLS 7 0.512 0.122 -3.991 0.876 0.179 -0.693 0.816 0.314 -0.584 DOLS 8 0.521 0.123 -3.900 0.831 0.179 -0.948 0.904 0.307 -0.312 DOLS 9 0.530 0.122 -3.840 0.786 0.183 -1.169 1.047 0.320 0.148 DOLS 10 0.538 0.122 -3.780 0.749 0.191 -1.313 1.188 0.305 0.616 DOLS 11 0.547 0.123 -3.679 0.719 0.196 -1.430 1.237 0.305 0.777 DOLS 12 0.552 0.125 -3.590 0.669 0.193 -1.714 1.248 0.312 0.795 DOLS 13 0.551 0.125 -3.587 0.634 0.192 -1.910 1.318 0.302 1.054 DOLS 14 0.551 0.126 -3.581 0.617 0.195 -1.969 1.315 0.310 1.016 DOLS 15 0.556 0.128 -3.471 0.609 0.197 -1.987 1.294 0.315 0.932 DOLS 16 0.561 0.133 -3.307 0.579 0.198 -2.127 1.347 0.331 1.049 DOLS 17 0.563 0.139 -3.156 0.554 0.205 -2.181 1.358 0.313 1.142 DOLS 18 0.567 0.143 -3.035 0.529 0.213 -2.210 1.400 0.299 1.337 DOLS 19 0.577 0.145 -2.912 0.522 0.224 -2.135 1.498 0.283 1.760 DOLS 20 0.588 0.146 -2.824 0.504 0.231 -2.151 1.589 0.297 1.984 DGLS 1 0.272 0.073 -10.039 -0.045 0.042 -24.719 -0.167 0.263 -4.440 DGLS 2 0.410 0.096 -6.166 -0.057 0.078 -13.505 -0.307 0.429 -3.046 DGLS 3 0.584 0.114 -3.637 0.586 0.139 -2.980 0.865 0.577 -0.233 DGLS 4 0.501 0.128 -3.903 0.758 0.170 -1.422 1.112 0.577 0.195 DGLS 5 0.548 0.143 -3.165 0.772 0.195 -1.172 1.205 0.576 0.357 DGLS 6 0.503 0.155 -3.205 0.766 0.212 -1.103 1.208 0.579 0.360 DGLS 7 0.458 0.168 -3.232 0.867 0.230 -0.578 1.717 0.740 0.969 DGLS 8 0.477 0.175 -2.987 0.796 0.241 -0.849 1.673 0.714 0.942 DGLS 9 0.500 0.180 -2.784 0.716 0.244 -1.168 1.662 0.709 0.933 DGLS 10 0.476 0.189 -2.780 0.667 0.251 -1.328 1.664 0.689 0.964 DGLS 11 0.550 0.190 -2.369 0.753 0.261 -0.948 1.728 0.702 1.037 DGLS 12 0.637 0.195 -1.862 0.622 0.255 -1.482 1.676 0.746 0.905 DGLS 13 0.624 0.201 -1.871 0.541 0.252 -1.820 1.804 0.803 1.001 DGLS 14 0.565 0.210 -2.073 0.491 0.260 -1.957 1.913 0.849 1.075 DGLS 15 0.588 0.215 -1.916 0.520 0.267 -1.800 1.687 0.960 0.716 DGLS 16 0.609 0.218 -1.794 0.500 0.283 -1.766 1.985 1.014 0.971 DGLS 17 0.580 0.226 -1.857 0.475 0.294 -1.787 2.115 1.096 1.017 DGLS 18 0.550 0.237 -1.900 0.419 0.308 -1.885 2.431 1.227 1.166 DGLS 19 0.525 0.247 -1.922 0.440 0.322 -1.742 2.506 1.298 1.161 DGLS 20 0.480 0.263 -1.980 0.417 0.334 -1.746 2.441 1.200 1.201 Notes 1. The Newey and West (1987) method is employed in the DOLS(p) estimator. 2. An AR(1) model is assumed for the errors in the DGLS(p) estimator. 21 Table 1C: Estimation Results – Quarterly short-term interest rates Country Italy Netherlands Norway Estimator θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 OLS 0.480 0.122 -4.252 0.415 0.084 -6.964 0.547 0.106 -4.255 ADL(1,2) 0.999 0.239 -0.003 0.902 0.209 -0.469 1.135 0.573 0.235 JOH 1.014 0.164 0.088 0.998 0.190 -0.009 1.425 0.196 2.164 FMLS 0.594 0.108 -3.758 0.524 0.140 -3.405 0.795 0.177 -1.155 PW-FMLS 0.772 0.182 -1.250 0.806 0.192 -1.006 1.245 0.220 1.105 DOLS 1 0.532 0.119 -3.937 0.505 0.099 -5.027 0.712 0.143 -2.012 DOLS 2 0.568 0.113 -3.820 0.546 0.109 -4.174 0.799 0.164 -1.226 DOLS 3 0.595 0.101 -4.011 0.566 0.114 -3.827 0.855 0.173 -0.844 DOLS 4 0.615 0.091 -4.231 0.579 0.114 -3.676 0.876 0.171 -0.724 DOLS 5 0.634 0.081 -4.497 0.587 0.112 -3.689 0.911 0.162 -0.550 DOLS 6 0.645 0.075 -4.706 0.598 0.108 -3.713 0.963 0.148 -0.249 DOLS 7 0.657 0.070 -4.885 0.610 0.105 -3.722 0.999 0.134 -0.010 DOLS 8 0.659 0.070 -4.842 0.620 0.101 -3.747 1.014 0.125 0.115 DOLS 9 0.662 0.073 -4.644 0.629 0.098 -3.776 1.035 0.123 0.282 DOLS 10 0.659 0.075 -4.557 0.642 0.096 -3.737 1.056 0.124 0.451 DOLS 11 0.657 0.076 -4.499 0.659 0.094 -3.625 1.068 0.125 0.544 DOLS 12 0.659 0.076 -4.512 0.673 0.092 -3.542 1.071 0.126 0.562 DOLS 13 0.664 0.075 -4.490 0.689 0.092 -3.404 1.077 0.124 0.619 DOLS 14 0.673 0.074 -4.414 0.708 0.092 -3.186 1.094 0.118 0.790 DOLS 15 0.677 0.074 -4.343 0.729 0.093 -2.924 1.111 0.112 0.990 DOLS 16 0.676 0.076 -4.276 0.740 0.093 -2.779 1.115 0.109 1.055 DOLS 17 0.673 0.076 -4.313 0.748 0.095 -2.653 1.121 0.106 1.141 DOLS 18 0.671 0.077 -4.271 0.755 0.097 -2.533 1.129 0.102 1.270 DOLS 19 0.669 0.079 -4.187 0.764 0.098 -2.407 1.142 0.098 1.450 DOLS 20 0.673 0.079 -4.149 0.774 0.098 -2.301 1.148 0.097 1.522 DGLS 1 0.161 0.059 -14.144 0.174 0.045 -18.455 -0.014 0.045 -22.728 DGLS 2 0.235 0.101 -7.577 0.360 0.055 -11.606 -0.014 0.069 -14.757 DGLS 3 0.445 0.135 -4.105 0.423 0.070 -8.289 0.017 0.108 -9.076 DGLS 4 0.577 0.151 -2.812 0.511 0.082 -5.938 -0.074 0.130 -8.248 DGLS 5 0.666 0.154 -2.170 0.471 0.099 -5.357 -0.172 0.150 -7.816 DGLS 6 0.663 0.165 -2.043 0.458 0.113 -4.785 -0.164 0.175 -6.646 DGLS 7 0.791 0.180 -1.164 0.508 0.126 -3.903 0.076 0.201 -4.601 DGLS 8 0.853 0.179 -0.821 0.536 0.139 -3.327 0.165 0.218 -3.836 DGLS 9 0.949 0.199 -0.259 0.450 0.153 -3.603 0.214 0.239 -3.292 DGLS 10 1.094 0.225 0.418 0.365 0.170 -3.729 0.265 0.263 -2.793 DGLS 11 1.054 0.238 0.227 0.463 0.176 -3.048 0.517 0.294 -1.644 DGLS 12 0.958 0.223 -0.189 0.433 0.187 -3.041 0.310 0.315 -2.189 DGLS 13 0.931 0.224 -0.310 0.382 0.200 -3.086 -0.039 0.320 -3.252 DGLS 14 0.942 0.239 -0.243 0.429 0.206 -2.773 -0.145 0.343 -3.335 DGLS 15 0.951 0.243 -0.204 0.636 0.198 -1.833 -0.094 0.389 -2.811 DGLS 16 0.966 0.228 -0.148 0.794 0.206 -0.999 -0.160 0.416 -2.791 DGLS 17 0.965 0.232 -0.150 0.808 0.218 -0.884 -0.221 0.447 -2.732 DGLS 18 0.955 0.250 -0.179 0.764 0.226 -1.044 -0.394 0.480 -2.906 DGLS 19 0.956 0.264 -0.168 0.791 0.235 -0.891 1.176 0.232 0.760 DGLS 20 0.995 0.297 -0.016 0.776 0.244 -0.921 1.222 0.227 0.976 Notes 1. The Newey and West (1987) method is employed in the DOLS(p) estimator. 2. An AR(1) model is assumed for the errors in the DGLS(p) estimator. 22 Table 1D: Estimation Results – Quarterly short-term interest rates Country Portugal Sweden Switzerland Estimator θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 OLS 0.517 0.114 -4.255 0.579 0.077 -5.466 0.596 0.089 -4.501 ADL(1,2) 1.107 0.258 0.416 0.975 0.399 -0.063 0.860 0.209 -0.669 JOH 1.254 0.129 1.976 1.352 0.147 2.394 1.344 0.125 2.758 FMLS 0.716 0.157 -1.802 0.864 0.156 -0.867 0.776 0.149 -1.503 PW-FMLS 1.051 0.187 0.273 1.259 0.188 1.378 1.256 0.169 1.516 DOLS 1 0.651 0.124 -2.808 0.772 0.094 -2.437 0.742 0.100 -2.573 DOLS 2 0.866 0.119 -1.125 0.891 0.099 -1.095 0.858 0.105 -1.349 DOLS 3 0.906 0.099 -0.946 0.970 0.100 -0.303 0.913 0.118 -0.737 DOLS 4 0.921 0.090 -0.880 0.992 0.100 -0.077 0.915 0.121 -0.702 DOLS 5 0.914 0.091 -0.941 1.009 0.098 0.094 0.906 0.124 -0.762 DOLS 6 0.913 0.093 -0.943 1.042 0.092 0.457 0.892 0.128 -0.840 DOLS 7 0.913 0.094 -0.927 1.070 0.091 0.777 0.880 0.136 -0.887 DOLS 8 0.927 0.094 -0.785 1.071 0.092 0.771 0.874 0.139 -0.910 DOLS 9 0.935 0.094 -0.694 1.072 0.093 0.775 0.874 0.141 -0.897 DOLS 10 0.934 0.095 -0.701 1.075 0.096 0.783 0.884 0.137 -0.850 DOLS 11 0.933 0.096 -0.697 1.077 0.097 0.794 0.876 0.133 -0.934 DOLS 12 0.934 0.098 -0.671 1.078 0.099 0.784 0.848 0.130 -1.170 DOLS 13 0.944 0.098 -0.569 1.078 0.101 0.778 0.820 0.130 -1.388 DOLS 14 0.950 0.098 -0.508 1.083 0.102 0.809 0.807 0.132 -1.471 DOLS 15 0.947 0.101 -0.531 1.093 0.102 0.909 0.791 0.134 -1.554 DOLS 16 0.942 0.106 -0.553 1.103 0.100 1.026 0.788 0.141 -1.503 DOLS 17 0.947 0.109 -0.493 1.114 0.096 1.191 0.774 0.154 -1.467 DOLS 18 0.962 0.110 -0.344 1.124 0.091 1.371 0.759 0.170 -1.414 DOLS 19 0.981 0.110 -0.168 1.131 0.088 1.491 0.742 0.185 -1.396 DOLS 20 0.992 0.110 -0.074 1.143 0.083 1.719 0.737 0.197 -1.336 DGLS 1 -0.032 0.043 -23.845 -0.026 0.048 -21.275 0.075 0.048 -19.282 DGLS 2 -0.065 0.088 -12.078 -0.116 0.077 -14.520 0.020 0.078 -12.616 DGLS 3 0.093 0.159 -5.707 0.013 0.121 -8.185 0.383 0.120 -5.142 DGLS 4 0.352 0.188 -3.442 0.045 0.149 -6.431 0.624 0.145 -2.594 DGLS 5 0.460 0.199 -2.718 -0.127 0.164 -6.886 0.659 0.169 -2.020 DGLS 6 1.054 0.125 0.431 -0.018 0.185 -5.509 0.647 0.185 -1.908 DGLS 7 1.101 0.134 0.749 0.275 0.218 -3.329 0.553 0.200 -2.236 DGLS 8 1.128 0.141 0.912 0.363 0.247 -2.582 0.499 0.214 -2.345 DGLS 9 1.159 0.149 1.065 0.223 0.271 -2.868 0.471 0.224 -2.365 DGLS 10 1.170 0.157 1.083 0.960 0.221 -0.182 0.568 0.240 -1.800 DGLS 11 1.198 0.173 1.143 1.059 0.212 0.279 0.684 0.261 -1.209 DGLS 12 1.177 0.166 1.064 1.077 0.220 0.349 0.652 0.277 -1.258 DGLS 13 1.158 0.161 0.984 1.077 0.223 0.345 0.491 0.284 -1.792 DGLS 14 1.181 0.179 1.013 1.054 0.218 0.248 0.461 0.299 -1.802 DGLS 15 1.249 0.215 1.161 0.988 0.237 -0.051 0.364 0.306 -2.078 DGLS 16 1.194 0.208 0.934 0.037 0.396 -2.434 0.386 0.325 -1.890 DGLS 17 1.184 0.217 0.848 -0.043 0.419 -2.487 0.335 0.344 -1.934 DGLS 18 1.219 0.230 0.950 1.036 0.224 0.161 0.317 0.366 -1.866 DGLS 19 1.158 0.224 0.706 1.125 0.184 0.678 0.220 0.378 -2.065 DGLS 20 1.190 0.255 0.746 1.183 0.155 1.183 0.029 0.396 -2.455 Notes 1. The Newey and West (1987) method is employed in the DOLS(p) estimator. 2. An AR(1) model is assumed for the errors in the DGLS(p) estimator. 23 Table 1E: Estimation Results – Quarterly short-term interest rates Country UK US Estimator θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 OLS 0.416 0.052 -11.337 0.696 0.092 -3.301 ADL(1,2) 0.912 0.137 -0.645 1.053 0.197 0.267 JOH 1.092 0.105 0.874 1.451 0.174 2.599 FMLS 0.583 0.119 -3.503 0.802 0.149 -1.326 PW-FMLS 0.926 0.149 -0.493 1.218 0.165 1.322 DOLS 1 0.602 0.081 -4.933 0.783 0.100 -2.163 DOLS 2 0.691 0.090 -3.455 0.846 0.109 -1.414 DOLS 3 0.746 0.102 -2.493 0.872 0.114 -1.121 DOLS 4 0.748 0.101 -2.488 0.887 0.122 -0.931 DOLS 5 0.751 0.101 -2.472 0.900 0.129 -0.779 DOLS 6 0.764 0.097 -2.440 0.917 0.134 -0.618 DOLS 7 0.777 0.091 -2.461 0.930 0.140 -0.502 DOLS 8 0.781 0.088 -2.491 0.947 0.146 -0.363 DOLS 9 0.783 0.088 -2.478 0.962 0.148 -0.256 DOLS 10 0.779 0.089 -2.481 0.977 0.150 -0.156 DOLS 11 0.780 0.089 -2.478 0.990 0.154 -0.066 DOLS 12 0.780 0.089 -2.456 1.004 0.157 0.024 DOLS 13 0.781 0.090 -2.442 1.012 0.158 0.077 DOLS 14 0.781 0.090 -2.427 1.025 0.158 0.161 DOLS 15 0.781 0.090 -2.431 1.037 0.160 0.231 DOLS 16 0.783 0.090 -2.408 1.056 0.161 0.346 DOLS 17 0.786 0.090 -2.390 1.077 0.163 0.471 DOLS 18 0.783 0.092 -2.372 1.089 0.165 0.540 DOLS 19 0.779 0.094 -2.348 1.096 0.166 0.581 DOLS 20 0.775 0.096 -2.333 1.110 0.168 0.654 DGLS 1 0.041 0.036 -26.561 0.158 0.059 -14.185 DGLS 2 0.120 0.052 -16.974 0.357 0.094 -6.871 DGLS 3 0.460 0.075 -7.241 0.549 0.116 -3.900 DGLS 4 0.440 0.087 -6.462 0.616 0.133 -2.888 DGLS 5 0.396 0.096 -6.296 0.634 0.143 -2.560 DGLS 6 0.371 0.110 -5.738 0.718 0.152 -1.863 DGLS 7 0.578 0.121 -3.478 0.687 0.162 -1.936 DGLS 8 0.710 0.120 -2.413 0.737 0.170 -1.547 DGLS 9 0.835 0.118 -1.402 0.761 0.179 -1.339 DGLS 10 0.736 0.132 -1.996 0.746 0.192 -1.324 DGLS 11 0.712 0.146 -1.972 0.704 0.208 -1.423 DGLS 12 0.789 0.142 -1.491 0.827 0.214 -0.809 DGLS 13 0.800 0.146 -1.373 0.826 0.225 -0.772 DGLS 14 0.852 0.145 -1.020 0.877 0.233 -0.528 DGLS 15 0.892 0.151 -0.716 0.772 0.257 -0.887 DGLS 16 0.907 0.160 -0.584 0.718 0.277 -1.021 DGLS 17 0.890 0.161 -0.686 0.981 0.253 -0.074 DGLS 18 0.885 0.162 -0.709 1.075 0.257 0.291 DGLS 19 0.910 0.172 -0.524 1.025 0.270 0.092 DGLS 20 0.962 0.200 -0.191 1.026 0.279 0.092 Notes 1. The Newey and West (1987) method is employed in the DOLS(p) estimator. 2. An AR(1) model is assumed for the errors in the DGLS(p) estimator. 24 Table 2A: Estimation Results – Annual long-term interest rates Country Australia Belgium Canada Estimator θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 OLS 0.251 0.185 -4.062 0.450 0.165 -3.345 0.574 0.151 -2.821 ADL(1,2) 1.166 0.353 0.469 0.761 0.356 -0.672 1.032 0.254 0.126 JOH 1.561 0.313 1.792 1.779 0.372 2.093 1.068 0.178 0.384 FMLS 0.368 0.170 -3.717 0.714 0.128 -2.241 0.900 0.215 -0.464 PW-FMLS 1.337 0.296 1.140 1.007 0.203 0.032 1.234 0.205 1.142 DOLS 1 0.314 0.197 -3.488 0.535 0.193 -2.415 0.661 0.141 -2.398 DOLS 2 0.507 0.160 -3.083 0.598 0.214 -1.879 0.734 0.144 -1.841 DOLS 3 0.623 0.172 -2.190 0.641 0.210 -1.713 0.826 0.148 -1.175 DOLS 4 0.687 0.178 -1.761 0.710 0.202 -1.434 0.856 0.132 -1.092 DOLS 5 0.745 0.173 -1.472 0.760 0.178 -1.344 0.882 0.107 -1.097 DOLS 6 0.814 0.149 -1.249 0.827 0.140 -1.238 0.909 0.082 -1.099 DOLS 7 0.898 0.125 -0.817 0.887 0.108 -1.043 0.932 0.080 -0.856 DOLS 8 0.955 0.106 -0.429 0.914 0.097 -0.890 0.961 0.089 -0.436 DOLS 9 1.019 0.090 0.209 0.949 0.089 -0.574 0.963 0.085 -0.438 DOLS 10 1.067 0.090 0.744 0.968 0.097 -0.334 0.964 0.089 -0.407 DOLS 11 1.106 0.083 1.284 0.962 0.119 -0.325 0.981 0.101 -0.193 DOLS 12 1.117 0.082 1.435 0.955 0.141 -0.321 0.989 0.104 -0.109 DOLS 13 1.125 0.097 1.286 0.924 0.171 -0.445 1.039 0.119 0.326 DOLS 14 1.144 0.117 1.230 0.911 0.197 -0.451 1.083 0.147 0.561 DOLS 15 1.146 0.153 0.954 0.856 0.215 -0.669 1.082 0.178 0.462 DOLS 16 1.151 0.154 0.981 0.781 0.211 -1.039 1.088 0.209 0.419 DOLS 17 1.176 0.160 1.098 0.820 0.235 -0.767 1.096 0.234 0.409 DOLS 18 1.192 0.165 1.162 0.883 0.254 -0.463 1.071 0.259 0.273 DOLS 19 1.271 0.182 1.491 1.030 0.312 0.097 1.110 0.333 0.330 DOLS 20 1.220 0.233 0.941 1.268 0.373 0.719 1.193 0.411 0.470 DGLS 1 0.174 0.058 -14.216 0.212 0.075 -10.572 0.234 0.083 -9.285 DGLS 2 0.298 0.089 -7.887 0.355 0.110 -5.882 0.441 0.110 -5.065 DGLS 3 0.315 0.115 -5.982 0.276 0.128 -5.635 0.579 0.130 -3.231 DGLS 4 0.388 0.137 -4.469 0.243 0.186 -4.079 0.633 0.161 -2.278 DGLS 5 0.385 0.161 -3.825 0.223 0.224 -3.479 0.700 0.163 -1.843 DGLS 6 0.448 0.174 -3.169 0.436 0.243 -2.327 0.791 0.173 -1.207 DGLS 7 0.659 0.174 -1.961 0.785 0.201 -1.071 0.859 0.160 -0.885 DGLS 8 0.808 0.143 -1.343 0.812 0.213 -0.886 0.916 0.104 -0.810 DGLS 9 0.955 0.104 -0.437 0.924 0.158 -0.480 0.925 0.101 -0.736 DGLS 10 1.050 0.079 0.634 1.046 0.163 0.284 0.971 0.125 -0.232 DGLS 11 1.110 0.075 1.472 1.088 0.175 0.501 0.988 0.131 -0.091 DGLS 12 1.113 0.082 1.378 0.971 0.189 -0.156 0.983 0.148 -0.116 DGLS 13 1.115 0.088 1.306 0.974 0.218 -0.122 1.058 0.163 0.358 DGLS 14 1.138 0.099 1.387 1.090 0.244 0.367 1.085 0.177 0.481 DGLS 15 1.141 0.105 1.337 1.036 0.268 0.133 1.088 0.197 0.448 DGLS 16 1.135 0.127 1.062 0.969 0.318 -0.099 1.126 0.241 0.523 DGLS 17 1.163 0.157 1.041 1.000 0.365 0.000 1.151 0.267 0.565 DGLS 18 1.170 0.192 0.885 1.015 0.456 0.033 1.196 0.334 0.586 DGLS 19 1.279 0.236 1.182 1.452 0.414 1.091 1.408 0.407 1.002 DGLS 20 1.334 0.267 1.252 1.912 0.414 2.205 1.579 0.530 1.092 Notes 1. The Newey and West (1987) method is employed in the DOLS(p) estimator. 2. An AR(1) model is assumed for the errors in the DGLS(p) estimator. 25 Table 2B: Estimation Results – Annual long-term interest rates Country France Germany Ireland Estimator θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) t-test Ho: θ ˆ=1 OLS 0.334 0.151 -4.425 0.615 0.092 -4.196 0.551 0.054 -8.295 ADL(1,2) 0.767 0.283 -0.824 0.675 0.205 -1.587 0.686 0.127 -2.470 JOH 1.185 0.186 0.996 0.818 0.1383 -1.317 0.892 0.109 -0.993 FMLS 0.515 0.143 -3.397 1.136 0.277 0.490 0.833 0.156 -1.071 PW-FMLS 0.870 0.168 -0.772 1.622 0.303 2.052 1.047 0.158 0.299 DOLS 1 0.421 0.170 -3.398 0.645 0.098 -3.614 0.577 0.060 -7.064 DOLS 2 0.529 0.157 -3.002 0.662 0.119 -2.844 0.646 0.069 -5.138 DOLS 3 0.640 0.142 -2.541 0.613 0.130 -2.973 0.687 0.068 -4.588 DOLS 4 0.674 0.136 -2.392 0.574 0.147 -2.902 0.706 0.065 -4.554 DOLS 5 0.729 0.134 -2.032 0.604 0.151 -2.629 0.726 0.062 -4.440 DOLS 6 0.778 0.132 -1.687 0.618 0.144 -2.643 0.730 0.060 -4.520 DOLS 7 0.810 0.133 -1.424 0.653 0.145 -2.399 0.754 0.057 -4.337 DOLS 8 0.836 0.135 -1.218 0.705 0.131 -2.252 0.774 0.054 -4.195 DOLS 9 0.947 0.136 -0.389 0.766 0.119 -1.971 0.780 0.052 -4.208 DOLS 10 0.994 0.124 -0.049 0.813 0.135 -1.393 0.813 0.054 -3.446 DOLS 11 1.043 0.125 0.341 0.842 0.164 -0.963 0.842 0.056 -2.843 DOLS 12 1.082 0.134 0.614 0.811 0.200 -0.949 0.866 0.061 -2.188 DOLS 13 1.114 0.145 0.782 0.793 0.269 -0.768 0.864 0.075 -1.805 DOLS 14 1.105 0.147 0.715 0.847 0.322 -0.477 0.927 0.099 -0.732 DOLS 15 1.131 0.163 0.800 0.889 0.397 -0.281 0.884 0.119 -0.976 DOLS 16 1.131 0.161 0.814 0.852 0.480 -0.309 0.857 0.089 -1.611 DOLS 17 0.997 0.177 -0.020 0.769 0.474 -0.487 0.804 0.093 -2.116 DOLS 18 1.068 0.217 0.313 0.776 0.394 -0.569 0.806 0.094 -2.067 DOLS 19 1.178 0.227 0.784 1.149 0.248 0.599 0.727 0.124 -2.203 DOLS 20 1.478 0.255 1.872 1.141 0.216 0.652 0.755 0.164 -1.500 DGLS 1 0.147 0.063 -13.457 0.567 0.126 -3.436 0.319 0.087 -7.809 DGLS 2 0.255 0.089 -8.395 0.698 0.149 -2.036 0.367 0.108 -5.886 DGLS 3 0.392 0.117 -5.218 0.646 0.167 -2.128 0.534 0.110 -4.222 DGLS 4 0.372 0.140 -4.485 0.523 0.180 -2.651 0.612 0.104 -3.746 DGLS 5 0.441 0.171 -3.270 0.519 0.195 -2.464 0.683 0.095 -3.335 DGLS 6 0.639 0.184 -1.970 0.569 0.220 -1.965 0.675 0.095 -3.411 DGLS 7 0.695 0.191 -1.595 0.510 0.258 -1.896 0.699 0.081 -3.694 DGLS 8 0.777 0.134 -1.672 0.640 0.265 -1.361 0.738 0.071 -3.689 DGLS 9 0.857 0.143 -1.000 0.709 0.275 -1.058 0.751 0.070 -3.552 DGLS 10 0.891 0.173 -0.629 0.823 0.284 -0.625 0.795 0.069 -2.988 DGLS 11 0.968 0.146 -0.222 0.794 0.292 -0.706 0.820 0.074 -2.445 DGLS 12 1.028 0.132 0.212 0.769 0.318 -0.725 0.845 0.080 -1.952 DGLS 13 1.092 0.144 0.639 0.744 0.385 -0.665 0.844 0.092 -1.693 DGLS 14 1.060 0.175 0.343 0.730 0.420 -0.643 0.887 0.116 -0.976 DGLS 15 1.046 0.168 0.273 0.903 0.535 -0.181 0.863 0.099 -1.382 DGLS 16 1.104 0.196 0.530 1.017 0.578 0.030 0.834 0.110 -1.503 DGLS 17 1.049 0.247 0.200 0.976 0.500 -0.049 0.831 0.131 -1.296 DGLS 18 1.013 0.343 0.039 1.365 0.420 0.869 0.777 0.146 -1.532 DGLS 19 0.844 0.501 -0.310 1.590 0.571 1.035 0.759 0.188 -1.285 DGLS 20 1.108 0.533 0.202 1.273 0.526 0.520 0.928 0.191 -0.376 Notes 1. The Newey and West (1987) method is employed in the DOLS(p) estimator. 2. An AR(1) model is assumed for the errors in the DGLS(p) estimator.